Solve for $x$ and $y$ using elimination. $\begin{align*}-4x+5y &= -2 \\ -4x+6y &= -8\end{align*}$
Explanation: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-1$ and the bottom equation by $1$ $\begin{align*}4x-5y &= 2\\ -4x+6y &= -8\end{align*}$ Add the top and bottom equations. $y = -6$ Substitute $-6$ for $y$ in the top equation. $-4x+5( -6) = -2$ $-4x-30 = -2$ $-4x = 28$ $x = -7$ The solution is $\enspace x = -7, \enspace y = -6$.